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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Bohr’s power series theorem in several variables
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by Harold P. Boas and Dmitry Khavinson
Proc. Amer. Math. Soc. 125 (1997), 2975-2979
DOI: https://doi.org/10.1090/S0002-9939-97-04270-6

Abstract:

Generalizing a classical one-variable theorem of Bohr, we show that if an $n$-variable power series has modulus less than $1$ in the unit polydisc, then the sum of the moduli of the terms is less than $1$ in the polydisc of radius $1/(3\sqrt n )$.
References
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Bibliographic Information
  • Harold P. Boas
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843–3368
  • MR Author ID: 38310
  • ORCID: 0000-0002-5031-3414
  • Email: boas@math.tamu.edu
  • Dmitry Khavinson
  • Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
  • MR Author ID: 101045
  • Email: dmitry@comp.uark.edu
  • Received by editor(s): May 8, 1996
  • Additional Notes: The first author’s research was supported in part by NSF grant number DMS 9500916 and in part at the Mathematical Sciences Research Institute by NSF grant number DMS 9022140.
  • Communicated by: Theodore W. Gamelin
  • © Copyright 1997 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 125 (1997), 2975-2979
  • MSC (1991): Primary 32A05
  • DOI: https://doi.org/10.1090/S0002-9939-97-04270-6
  • MathSciNet review: 1443371